A framework of a general type of Petrovsky equation is formulated. The characteristic equation for eigenvalues of the system is derived and the associated eigenfunctions are found. For N connected beams with linear feedbacks at joint points, the asymptotic expansions of eigenvalues and eigenfunctions are further developed, and the Riesz basis property and the exponential stability are then conc...

recently, mohiuddine and alghamdi introduced the notion of lacunary statistical convergence in a locally solid riesz space and established some results related to this concept. in this paper, some inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences are established and extensions of a decomposition theorem, a tauberian theorem to the l...

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-valued (primary) wavelet basis of L(2) (R(2)) into a complex one. The Riesz operator is also steerable in the sense that it give access to the Hil...

It is known [6], [14], [19] that if Ω⊂Rd belongs to a class of k-tiling domains when translated by lattice Λ, there exists Riesz basis exponentials for L2(Ω) constructed using k translates the dual Λ⁎. In this paper, we give an explicit construction corresponding biorthogonal basis. We also extend iterative reconstruction algorithm introduced in [11] setting.

Spectral problem for the Dirac operator with regular but not strongly boundary conditions and complex-valued potential summable over a finite interval is considered. The purpose of this paper to find under which root function system forms usual Riesz basis rather than parentheses.

In this paper, we show how to construct an orthonormal basis from Riesz by assuming that the fractional translates of a single function in core subspace multiresolution analysis form instead basis. definition analysis, intersection triviality condition follows other conditions. Furthermore, union density also under assumption Fourier transform scaling is continuous at 0. At culmination, provide...

Recently, we presented a new image pyramid, called the Riesz pyramid, that uses the Riesz transform to manipulate the phase in non-oriented sub-bands of an image sequence to produce real-time motion-magnified videos. In this report we give a quaternionic formulation of the Riesz pyramid, and show how several seemingly heuristic choices in how to use the Riesz transform for phase-based video mag...